Finite Group Databasebeta

← #22613523

Subgroups — #22613523

Order 9344.

564 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556590C211yesmaximal, characteristic, complemented
2C2×#14556568C211yesmaximal, characteristic
3C2×#14556568C211yesmaximal, characteristic
4C2×#14556556C211yesmaximal, characteristic, complemented
5#17988521C211yesmaximal, characteristic, complemented
6#17988517C211yesmaximal, characteristic, complemented
7#17988510C211yesmaximal, characteristic
8#17988491C211yesmaximal, characteristic, complemented
9#17988486C211yesmaximal, characteristic, complemented
10#17988482C211yesmaximal, characteristic, complemented
11#17988482C211yesmaximal, characteristic, complemented
12#17988481C211yesmaximal, characteristic
13#17988475C211yesmaximal, characteristic
14C22⋊C4×Dic73C211yesmaximal, characteristic
15#396×C73C211yesmaximal, characteristic
16C22×Dic146C2211yescharacteristic
17C22×Dic146C2211yescharacteristic
18C23×Dic73C2211yescharacteristic
19#14556590—24no—
20#14556568—24no—
21#14556568—24no—
22#14556556—24no—
23C2×C4⋊Dic73C2211yescharacteristic
24C2×C4⋊Dic73C2211yescharacteristic
25C2×C4⋊Dic73C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×#11924007C2211yescharacteristic
30C2×#11924007C2211yescharacteristic
31C2×#11924007C2211yescharacteristic
32C2×#11924007C2211yescharacteristic
33C2×#11924007C2211yescharacteristic
34C2×C22⋊Dic73C2211yescharacteristic
35C2×C22⋊Dic73C2211yescharacteristic
36C2×C22⋊Dic73C2211yescharacteristic
37C2×C4×Dic73C2211yescharacteristic
38C2×C4×Dic73C2211yescharacteristic
39C2×C4×Dic73C2211yescharacteristic
40C2×C4×Dic73C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46#14556498C2211yescharacteristic
47#14556498C2211yescharacteristic
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C4⋊C4×C73C2211yescharacteristic
50C2×C4⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C22⋊C4×C73C2211yescharacteristic
53C2×C22⋊C4×C73C2211yescharacteristic
54#95×C73C2211yescharacteristic
55C2×Dic146—22no—
56C2×Dic146—22no—
57C2×Dic146—22no—
58C2×Dic146—22no—
59C2×Dic146—22no—
60C2×Dic146D414yes—
61C22×Dic73—22no—
62C22×Dic73—22no—
63C22×Dic73—22no—
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C22×Dic73C2311yescharacteristic
69C22×Dic73C2311yescharacteristic
70C22×Dic73C2311yescharacteristic
71C22×Dic73C2311yescharacteristic
72C4⋊Dic73—22no—
73C4⋊Dic73—22no—
74C4⋊Dic73—22no—
75#11924007—22no—
76#11924007—22no—
77#11924007—22no—
78#11924007—22no—
79#11924007—22no—
80#11924007—22no—
81#11924007—22no—
82#11924007D414yes—
83C22⋊Dic73—22no—
84C22⋊Dic73—22no—
85C22⋊Dic73Q814yescomplemented
86C4×Dic73—22no—
87C4×Dic73—22no—
88C4×Dic73—22no—
89C4×Dic73—22no—
90C24×C73C2311yescharacteristic
91C22×C4×C73C2311yescharacteristic
92C22×C4×C73C2311yescharacteristic
93C22×C4×C73C2311yescharacteristic
94C22×C4×C73C2311yescharacteristic
95C22×C4×C73C2311yescharacteristic
96C22×C4×C73C2311yescharacteristic
97C4⋊C4×C73—22no—
98C4⋊C4×C73—22no—
99C4⋊C4×C73—22no—
100C22⋊C4×C73—22no—
101C22⋊C4×C73—22no—
102C22⋊C4×C73—22no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73C2×Q812yes—
110C23×C73C2411yescharacteristic
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73C2×D412yes—
127C2×C4×C73C2×D412yes—
128C2×C4×C73#4112yes—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—44no—
147C2×Dic73C2×D412yes—
148C2×Dic73C2×D412yes—
149C2×Dic73C2×D412yes—
150C2×Dic73C2×D412yes—
151C2×Dic73C2×Q812yes—
152C2×Dic73C2×Q812yes—
153C2×Dic73#4112yes—
154Dic146—28no—
155Dic146—44no—
156C22×C73—22no—
157C22×C73—22no—
158C22×C73—22no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73C22×D411yescharacteristic
164C22×C73C22×D411yescharacteristic
165C22×C73C22×Q811yescharacteristic
166C22×C73C2×#4111yescharacteristic
167C22×C73C2×#4111yescharacteristic
168C22×C732−1+411yescharacteristic
169C22×C732−1+411yescharacteristic
170C4×C73—22no—
171C4×C73—22no—
172C4×C73—22no—
173C4×C73—41no—
174C4×C73—41no—
175C4×C73—41no—
176Dic73—22no—
177Dic73—22no—
178Dic73—22no—
179Dic73—22no—
180Dic73—41no—
181Dic73—41no—
182Dic73—41no—
183Dic73#12114yes—
184C2×C73—42no—
185C2×C73C2×#12111yescharacteristic
186C2×C73#53311yescharacteristic
187C2×C73#54111yescharacteristic
188C2×C73#54711yescharacteristic
189C2×C73#54811yescharacteristic
190C2×C73D4×Q811yescharacteristic
191C2×C73D4×Q811yescharacteristic
192#2429—731nomaximal, Sylow
193C73#242911yescharacteristic, complemented, Sylow
194C2×C4⋊Q8—731no—
195C2×C22⋊Q8—731no—
196C2×C22⋊Q8—731no—
197C2×C4×Q8—731no—
198#398—731no—
199#398—731no—
200#396—731no—
201#396D7311yescharacteristic
202#391—731no—
203#389—731no—
204#389—731no—
205#389—731no—
206#388—731no—
207#388—731no—
208C4×C22⋊C4—731no—
209C22×Q8—731no—
210C22×Q8—731no—
211C23×C4—731no—
212C4⋊Q8—1464no—
213C22⋊Q8—1464no—
214C22⋊Q8—1464no—
215C4×Q8—1464no—
216C2×C4⋊C4—731no—
217C2×C4⋊C4—731no—
218C2×C4⋊C4—731no—
219C2×C4⋊C4—731no—
220C2×C4⋊C4—731no—
221C2×C4⋊C4—731no—
222C2×C4⋊C4—731no—
223C2×C4⋊C4—731no—
224C2×C4⋊C4—731no—
225C2×C4⋊C4—731no—
226C2×C4⋊C4—731no—
227C2×C4⋊C4C2×D7311yescharacteristic
228C2×C4⋊C4C2×D7311yescharacteristic
229C2×C4⋊C4C2×D7311yescharacteristic
230C2×C22⋊C4—731no—
231C2×C22⋊C4—731no—
232C2×C22⋊C4—731no—
233C2×C22⋊C4C2×D7311yescharacteristic
234C2×C22⋊C4C2×D7311yescharacteristic
235C2×C22⋊C4C2×D7311yescharacteristic
236C2×C42—731no—
237C2×C42—731no—
238C2×C42—731no—
239C2×C42—731no—
240#95—731no—
241#95—731no—
242#95—731no—
243#95—731no—
244#95—731no—
245#95—731no—
246#95—731no—
247#95C2×D7311yescharacteristic
248C24C22×D7311yescharacteristic
249C2×Q8—734no—
250C2×Q8—1462no—
251C2×Q8—1462no—
252C2×Q8—1462no—
253C2×Q8—1462no—
254C2×Q8—1462no—
255C22×C4—731no—
256C22×C4—731no—
257C22×C4—731no—
258C22×C4—731no—
259C22×C4—731no—
260C22×C4—731no—
261C22×C4—731no—
262C22×C4—731no—
263C22×C4—1462no—
264C22×C4—1462no—
265C22×C4—1462no—
266C22×C4C22×D7311yescharacteristic
267C22×C4C22×D7311yescharacteristic
268C22×C4C22×D7311yescharacteristic
269C22×C4C22×D7311yescharacteristic
270C22×C4C22×D7311yescharacteristic
271C22×C4C22×D7311yescharacteristic
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—734no—
276C4⋊C4—1462no—
277C4⋊C4—1462no—
278C4⋊C4—1462no—
279C4⋊C4—1462no—
280C4⋊C4—1462no—
281C4⋊C4—1462no—
282C4⋊C4—1462no—
283C4⋊C4—1462no—
284C4⋊C4—1462no—
285C4⋊C4—1462no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—734no—
290C22⋊C4—1462no—
291C22⋊C4—1462no—
292C42—1462no—
293C42—1462no—
294C42—1462no—
295C42—1462no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23Q8×D7312yes—
303C23C23×D7311yescharacteristic
304Q8—2924no—
305Q8—1468no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—2924no—
322C2×C4—732no—
323C2×C4—732no—
324C2×C4—732no—
325C2×C4—732no—
326C2×C4—732no—
327C2×C4—732no—
328C2×C4—732no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4—1461no—
333C2×C4—1461no—
334C2×C4—1461no—
335C2×C4—1461no—
336C2×C4—1461no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4—1461no—
346C2×C4D4×D7312yes—
347C2×C4D4×D7312yes—
348C2×C4#1192402712yes—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22C2×D4×D7311yescharacteristic
357C22C2×D4×D7311yescharacteristic
358C22C2×Q8×D7311yescharacteristic
359C22#41×D7311yescharacteristic
360C22C2×#1192402711yescharacteristic
361C22#1455663811yescharacteristic
362C22#1455663811yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—2921no—
370C4—2921no—
371C4—2921no—
372C4—734no—
373C4—1462no—
374C4—1462no—
375C4—1462no—
376C4—1462no—
377C2—42no—
378C2#121×D7311yescharacteristic
379C2#1798913911yescharacteristic
380C2#1798919411yescharacteristic
381C2#1798923711yescharacteristic
382C2#1798924311yescharacteristic
383C2#1798925011yescharacteristic
384C2#1798925011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#396×C73C2
hypercenter#396D73
hypocenterC73#2429
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #396

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14556590C2semidirect
4. C2×#14556556C2semidirect
5. #17988521C2semidirect
6. #17988517C2semidirect
8. #17988491C2semidirect
9. #17988486C2semidirect
10. #17988482C2semidirect
11. #17988482C2semidirect
85. C22⋊Dic73Q8semidirect
193. C73#2429semidirect